Question

Mr. Brown has taken out a loan of value $1,000 with a 5% APR. He has been paying off the loan at a constant rate of r = $150/year. Set up a linear ODE for the balance of the loan P(t) as a function of time t in years. [If you're having trouble getting started, please see Example 2 from

Answer 1

Answer:

$\frac{dp}{dt}$ = 0.05P - 150

Step-by-step explanation:

Let P(t) be the balance of the loan at time t years,

Let P(t) will satisfy $\frac{dp}{dt}=rP-R$

where r = annual interest rate

          R = per year payment rate

          R = $150/year

          r = $\frac{5}{100}$ = 0.05  $\frac{5}{100}$

Now we have the following picture,

Interest            Balance          Payment

5%           ⇒          P(t)       ⇒     $150/year

(0.05)

Therefore, a linear ODE satisfied by P(t) is given by

$\frac{dp}{dt}$ = 0.05P - 150